ABSTRACT The internal working of low-mass stars is of great significance to both the study of stellar structure and the history of the Milky Way. Asteroseismology has the power to directly sense the internal structure of stars and allows for the determination of the evolutionary state – i.e. has helium burning commenced or is the energy generated only by the fusion in the hydrogen-burning shell? We use observational data from red-giant stars in a combination (known as APOKASC) of asteroseismology (from the Kepler mission) and spectroscopy (from SDSS/APOGEE). The new feature of the analysis is that the APOKASC evolutionary state determination is based on the comparison of diverse approaches to the investigation of the frequency-power spectrum. The high level of agreement between the methods is a strong validation of the approaches. Stars for which there is not a consensus view are readily identified. The comparison also facilitates the identification of unusual stars including those that show evidence for very strong coupling between p and g cavities. The comparison between the classification based on the spectroscopic data and asteroseismic data have led to a new value for the statistical uncertainty in APOGEE temperatures. These consensus evolutionary states will be used as an input for methods that derive masses and ages for these stars based on comparison of observables with stellar evolutionary models (‘grid-based modelling’) and as a training set for machine-learning and other data-driven methods of evolutionary state determination.